Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(62.2833135766\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 6x - 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.76156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.76156 | −1.04377 | −0.521885 | − | 0.853016i | \(-0.674771\pi\) | ||||
−0.521885 | + | 0.853016i | \(0.674771\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.49084 | 1.35404 | 0.677019 | − | 0.735965i | \(-0.263271\pi\) | ||||
0.677019 | + | 0.735965i | \(0.263271\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.62620 | −0.879482 | −0.439741 | − | 0.898125i | \(-0.644930\pi\) | ||||
−0.439741 | + | 0.898125i | \(0.644930\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.14931 | −1.41075 | −0.705375 | − | 0.708835i | \(-0.749221\pi\) | ||||
−0.705375 | + | 0.708835i | \(0.749221\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.76156 | −0.602621 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.52311 | −1.15165 | −0.575824 | − | 0.817573i | \(-0.695319\pi\) | ||||
−0.575824 | + | 0.817573i | \(0.695319\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.25240 | 1.16104 | 0.580520 | − | 0.814246i | \(-0.302849\pi\) | ||||
0.580520 | + | 0.814246i | \(0.302849\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.49084 | 1.52500 | 0.762500 | − | 0.646988i | \(-0.223972\pi\) | ||||
0.762500 | + | 0.646988i | \(0.223972\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.49084 | 0.781755 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.896916 | 0.147452 | 0.0737261 | − | 0.997279i | \(-0.476511\pi\) | ||||
0.0737261 | + | 0.997279i | \(0.476511\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.89692 | 0.452422 | 0.226211 | − | 0.974078i | \(-0.427366\pi\) | ||||
0.226211 | + | 0.974078i | \(0.427366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.270718 | −0.0412841 | −0.0206421 | − | 0.999787i | \(-0.506571\pi\) | ||||
−0.0206421 | + | 0.999787i | \(0.506571\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.38776 | −0.494155 | −0.247077 | − | 0.968996i | \(-0.579470\pi\) | ||||
−0.247077 | + | 0.968996i | \(0.579470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.626198 | 0.0894569 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.62620 | −0.507769 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.27072 | 0.449268 | 0.224634 | − | 0.974443i | \(-0.427881\pi\) | ||||
0.224634 | + | 0.974443i | \(0.427881\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.14931 | −0.814496 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.53707 | −1.24162 | −0.620810 | − | 0.783961i | \(-0.713196\pi\) | ||||
−0.620810 | + | 0.783961i | \(0.713196\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4200 | 1.46219 | 0.731093 | − | 0.682278i | \(-0.239011\pi\) | ||||
0.731093 | + | 0.682278i | \(0.239011\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.76156 | −0.347924 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4340 | 1.51905 | 0.759526 | − | 0.650476i | \(-0.225431\pi\) | ||||
0.759526 | + | 0.650476i | \(0.225431\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.52311 | −0.664905 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.89692 | 1.05587 | 0.527935 | − | 0.849285i | \(-0.322967\pi\) | ||||
0.527935 | + | 0.849285i | \(0.322967\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.25240 | −0.380664 | −0.190332 | − | 0.981720i | \(-0.560956\pi\) | ||||
−0.190332 | + | 0.981720i | \(0.560956\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.4017 | −1.41331 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.6724 | 1.53827 | 0.769134 | − | 0.639087i | \(-0.220688\pi\) | ||||
0.769134 | + | 0.639087i | \(0.220688\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.03228 | 0.332835 | 0.166418 | − | 0.986055i | \(-0.446780\pi\) | ||||
0.166418 | + | 0.986055i | \(0.446780\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.25240 | 0.670327 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.20617 | −0.233853 | −0.116927 | − | 0.993141i | \(-0.537304\pi\) | ||||
−0.116927 | + | 0.993141i | \(0.537304\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.76156 | 0.289490 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.49084 | 0.880459 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.7572 | 1.80297 | 0.901485 | − | 0.432811i | \(-0.142478\pi\) | ||||
0.901485 | + | 0.432811i | \(0.142478\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.49084 | 0.451346 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.83237 | 0.580342 | 0.290171 | − | 0.956975i | \(-0.406288\pi\) | ||||
0.290171 | + | 0.956975i | \(0.406288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.45856 | 0.340782 | 0.170391 | − | 0.985376i | \(-0.445497\pi\) | ||||
0.170391 | + | 0.985376i | \(0.445497\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.832365 | 0.0804678 | 0.0402339 | − | 0.999190i | \(-0.487190\pi\) | ||||
0.0402339 | + | 0.999190i | \(0.487190\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.1493 | −1.16369 | −0.581847 | − | 0.813299i | \(-0.697670\pi\) | ||||
−0.581847 | + | 0.813299i | \(0.697670\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.896916 | 0.0851315 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.50479 | −0.423775 | −0.211888 | − | 0.977294i | \(-0.567961\pi\) | ||||
−0.211888 | + | 0.977294i | \(0.567961\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.0140 | 0.917978 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.16763 | 0.833421 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.89692 | 0.261206 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.62620 | −0.587980 | −0.293990 | − | 0.955808i | \(-0.594983\pi\) | ||||
−0.293990 | + | 0.955808i | \(0.594983\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.270718 | −0.0238354 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.10308 | 0.0963769 | 0.0481884 | − | 0.998838i | \(-0.484655\pi\) | ||||
0.0481884 | + | 0.998838i | \(0.484655\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.9817 | 1.47250 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.4479 | 1.74699 | 0.873493 | − | 0.486837i | \(-0.161850\pi\) | ||||
0.873493 | + | 0.486837i | \(0.161850\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.5693 | 1.40539 | 0.702697 | − | 0.711490i | \(-0.251979\pi\) | ||||
0.702697 | + | 0.711490i | \(0.251979\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.38776 | −0.285300 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.49084 | −0.375543 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.626198 | 0.0516479 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.79383 | 0.310803 | 0.155401 | − | 0.987851i | \(-0.450333\pi\) | ||||
0.155401 | + | 0.987851i | \(0.450333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.80779 | −0.472631 | −0.236315 | − | 0.971676i | \(-0.575940\pi\) | ||||
−0.236315 | + | 0.971676i | \(0.575940\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.62620 | −0.293161 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.6541 | −1.08972 | −0.544858 | − | 0.838528i | \(-0.683416\pi\) | ||||
−0.544858 | + | 0.838528i | \(0.683416\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.27072 | 0.259385 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.2524 | 1.20206 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.25240 | −0.568052 | −0.284026 | − | 0.958817i | \(-0.591670\pi\) | ||||
−0.284026 | + | 0.958817i | \(0.591670\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.14931 | 0.166319 | 0.0831594 | − | 0.996536i | \(-0.473499\pi\) | ||||
0.0831594 | + | 0.996536i | \(0.473499\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.14931 | −0.470250 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25.5693 | 1.94400 | 0.972001 | − | 0.234978i | \(-0.0755020\pi\) | ||||
0.972001 | + | 0.234978i | \(0.0755020\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.53707 | −0.716850 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.5510 | −1.61080 | −0.805399 | − | 0.592732i | \(-0.798049\pi\) | ||||
−0.805399 | + | 0.592732i | \(0.798049\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.607876 | −0.0451831 | −0.0225915 | − | 0.999745i | \(-0.507192\pi\) | ||||
−0.0225915 | + | 0.999745i | \(0.507192\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.4200 | 0.844193 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.2847 | −1.19085 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.76156 | −0.200874 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.2803 | −1.53979 | −0.769894 | − | 0.638171i | \(-0.779691\pi\) | ||||
−0.769894 | + | 0.638171i | \(0.779691\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.45856 | −0.536879 | −0.268440 | − | 0.963297i | \(-0.586508\pi\) | ||||
−0.268440 | + | 0.963297i | \(0.586508\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.45856 | 0.531401 | 0.265700 | − | 0.964056i | \(-0.414397\pi\) | ||||
0.265700 | + | 0.964056i | \(0.414397\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.3372 | 1.37077 | 0.685387 | − | 0.728179i | \(-0.259633\pi\) | ||||
0.685387 | + | 0.728179i | \(0.259633\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.4340 | 0.877026 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.2663 | −1.21186 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.52311 | −0.383883 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.6156 | −1.91021 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.02791 | −0.552664 | −0.276332 | − | 0.961062i | \(-0.589119\pi\) | ||||
−0.276332 | + | 0.961062i | \(0.589119\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.89692 | 0.609607 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.4479 | −1.59175 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.25240 | −0.219777 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.62620 | 0.243924 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.5048 | 1.10524 | 0.552621 | − | 0.833432i | \(-0.313628\pi\) | ||||
0.552621 | + | 0.833432i | \(0.313628\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.69701 | −0.179007 | −0.0895033 | − | 0.995987i | \(-0.528528\pi\) | ||||
−0.0895033 | + | 0.995987i | \(0.528528\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5616 | −0.697933 | −0.348967 | − | 0.937135i | \(-0.613467\pi\) | ||||
−0.348967 | + | 0.937135i | \(0.613467\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.4017 | −0.815973 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.2158 | 1.65194 | 0.825969 | − | 0.563715i | \(-0.190628\pi\) | ||||
0.825969 | + | 0.563715i | \(0.190628\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.6724 | 0.888120 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.51875 | −0.551032 | −0.275516 | − | 0.961297i | \(-0.588849\pi\) | ||||
−0.275516 | + | 0.961297i | \(0.588849\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.45856 | 0.480448 | 0.240224 | − | 0.970717i | \(-0.422779\pi\) | ||||
0.240224 | + | 0.970717i | \(0.422779\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.14931 | 0.391271 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.03228 | 0.192163 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.64452 | −0.608757 | −0.304378 | − | 0.952551i | \(-0.598449\pi\) | ||||
−0.304378 | + | 0.952551i | \(0.598449\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.8034 | −1.55938 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.3555 | −0.833092 | −0.416546 | − | 0.909115i | \(-0.636760\pi\) | ||||
−0.416546 | + | 0.909115i | \(0.636760\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.47689 | −0.153906 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.25240 | 0.387014 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.25240 | 0.570527 | 0.285264 | − | 0.958449i | \(-0.407919\pi\) | ||||
0.285264 | + | 0.958449i | \(0.407919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.20617 | −0.135015 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.2986 | 1.54248 | 0.771242 | − | 0.636542i | \(-0.219636\pi\) | ||||
0.771242 | + | 0.636542i | \(0.219636\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.3309 | 1.90322 | 0.951608 | − | 0.307314i | \(-0.0994300\pi\) | ||||
0.951608 | + | 0.307314i | \(0.0994300\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.76156 | 0.167137 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.0096 | 1.38251 | 0.691256 | − | 0.722610i | \(-0.257058\pi\) | ||||
0.691256 | + | 0.722610i | \(0.257058\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.49084 | 0.508333 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.19554 | −0.548560 | −0.274280 | − | 0.961650i | \(-0.588440\pi\) | ||||
−0.274280 | + | 0.961650i | \(0.588440\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.93545 | −0.590601 | −0.295301 | − | 0.955404i | \(-0.595420\pi\) | ||||
−0.295301 | + | 0.955404i | \(0.595420\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.85069 | −0.226511 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.7572 | 1.04094 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.7938 | 1.39005 | 0.695025 | − | 0.718985i | \(-0.255393\pi\) | ||||
0.695025 | + | 0.718985i | \(0.255393\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.49084 | 0.260585 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.52311 | 0.319410 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.747604 | 0.0430912 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.83237 | 0.335061 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.0664 | −1.43062 | −0.715309 | − | 0.698809i | \(-0.753714\pi\) | ||||
−0.715309 | + | 0.698809i | \(0.753714\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.45856 | 0.196751 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.3632 | 1.04128 | 0.520640 | − | 0.853776i | \(-0.325693\pi\) | ||||
0.520640 | + | 0.853776i | \(0.325693\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.7293 | −0.606455 | −0.303227 | − | 0.952918i | \(-0.598064\pi\) | ||||
−0.303227 | + | 0.952918i | \(0.598064\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.20617 | −0.460904 | −0.230452 | − | 0.973084i | \(-0.574021\pi\) | ||||
−0.230452 | + | 0.973084i | \(0.574021\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.0785 | 1.57209 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.832365 | 0.0464581 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.2986 | 1.24073 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.1493 | −0.671859 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.35548 | 0.515784 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.7110 | 1.68803 | 0.844014 | − | 0.536322i | \(-0.180187\pi\) | ||||
0.844014 | + | 0.536322i | \(0.180187\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.896916 | 0.0491507 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.13099 | 0.442923 | 0.221462 | − | 0.975169i | \(-0.428917\pi\) | ||||
0.221462 | + | 0.975169i | \(0.428917\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.50479 | −0.244667 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 38.1310 | 2.06491 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6016 | 0.950398 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.9248 | −0.801206 | −0.400603 | − | 0.916252i | \(-0.631199\pi\) | ||||
−0.400603 | + | 0.916252i | \(0.631199\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.5048 | −0.883481 | −0.441741 | − | 0.897143i | \(-0.645639\pi\) | ||||
−0.441741 | + | 0.897143i | \(0.645639\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.0664 | 1.22770 | 0.613851 | − | 0.789422i | \(-0.289619\pi\) | ||||
0.613851 | + | 0.789422i | \(0.289619\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.0140 | 0.529995 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.6681 | 1.72415 | 0.862077 | − | 0.506777i | \(-0.169163\pi\) | ||||
0.862077 | + | 0.506777i | \(0.169163\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8140 | 0.990213 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.16763 | 0.481176 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.1493 | −1.67818 | −0.839090 | − | 0.543992i | \(-0.816912\pi\) | ||||
−0.839090 | + | 0.543992i | \(0.816912\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.89692 | 0.150807 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.03228 | −0.468932 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.81404 | 0.352818 | 0.176409 | − | 0.984317i | \(-0.443552\pi\) | ||||
0.176409 | + | 0.984317i | \(0.443552\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.25240 | −0.322015 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.65078 | 0.0847948 | 0.0423974 | − | 0.999101i | \(-0.486500\pi\) | ||||
0.0423974 | + | 0.999101i | \(0.486500\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.62620 | −0.339470 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.0202 | 0.512009 | 0.256004 | − | 0.966676i | \(-0.417594\pi\) | ||||
0.256004 | + | 0.966676i | \(0.417594\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.270718 | −0.0137614 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.4017 | 0.983706 | 0.491853 | − | 0.870678i | \(-0.336320\pi\) | ||||
0.491853 | + | 0.870678i | \(0.336320\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.0279 | 1.01285 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.10308 | 0.0556432 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.56165 | −0.128565 | −0.0642827 | − | 0.997932i | \(-0.520476\pi\) | ||||
−0.0642827 | + | 0.997932i | \(0.520476\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.9817 | 0.850147 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.55102 | −0.177330 | −0.0886648 | − | 0.996062i | \(-0.528260\pi\) | ||||
−0.0886648 | + | 0.996062i | \(0.528260\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.49084 | −0.422959 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.02791 | 0.199656 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.0558 | 1.38727 | 0.693635 | − | 0.720326i | \(-0.256008\pi\) | ||||
0.693635 | + | 0.720326i | \(0.256008\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.4479 | 1.00862 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.3372 | 1.29597 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.5693 | 0.811404 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.3188 | 1.77429 | 0.887146 | − | 0.461490i | \(-0.152685\pi\) | ||||
0.887146 | + | 0.461490i | \(0.152685\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.2062 | 0.497418 | 0.248709 | − | 0.968578i | \(-0.419994\pi\) | ||||
0.248709 | + | 0.968578i | \(0.419994\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.38776 | −0.164718 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.5371 | −1.52619 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.49084 | −0.216820 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.8140 | −0.569062 | −0.284531 | − | 0.958667i | \(-0.591838\pi\) | ||||
−0.284531 | + | 0.958667i | \(0.591838\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.598291 | −0.0287521 | −0.0143760 | − | 0.999897i | \(-0.504576\pi\) | ||||
−0.0143760 | + | 0.999897i | \(0.504576\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33.9634 | 1.62469 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.6724 | −0.652549 | −0.326275 | − | 0.945275i | \(-0.605793\pi\) | ||||
−0.326275 | + | 0.945275i | \(0.605793\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.626198 | 0.0298190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.1772 | −1.52879 | −0.764393 | − | 0.644751i | \(-0.776961\pi\) | ||||
−0.764393 | + | 0.644751i | \(0.776961\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.79383 | 0.179442 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.81404 | −0.463153 | −0.231577 | − | 0.972817i | \(-0.574388\pi\) | ||||
−0.231577 | + | 0.972817i | \(0.574388\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.0096 | 0.612597 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.80779 | −0.272874 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5877 | 0.916272 | 0.458136 | − | 0.888882i | \(-0.348517\pi\) | ||||
0.458136 | + | 0.888882i | \(0.348517\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.62620 | −0.169256 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.7938 | 0.549294 | 0.274647 | − | 0.961545i | \(-0.411439\pi\) | ||||
0.274647 | + | 0.961545i | \(0.411439\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.8819 | −1.80700 | −0.903498 | − | 0.428592i | \(-0.859010\pi\) | ||||
−0.903498 | + | 0.428592i | \(0.859010\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.4017 | −1.17545 | −0.587725 | − | 0.809060i | \(-0.699976\pi\) | ||||
−0.587725 | + | 0.809060i | \(0.699976\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.3372 | −1.58554 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.6541 | −0.629148 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.21575 | −0.0559003 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.27072 | 0.149756 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.0987 | 1.55801 | 0.779005 | − | 0.627018i | \(-0.215725\pi\) | ||||
0.779005 | + | 0.627018i | \(0.215725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.896916 | −0.0408959 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.2524 | 0.694008 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.7616 | −0.759539 | −0.379769 | − | 0.925081i | \(-0.623997\pi\) | ||||
−0.379769 | + | 0.925081i | \(0.623997\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.25240 | −0.327965 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.65222 | 0.0745635 | 0.0372817 | − | 0.999305i | \(-0.488130\pi\) | ||||
0.0372817 | + | 0.999305i | \(0.488130\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.6724 | −1.02111 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.5693 | −1.10209 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.7326 | −1.01765 | −0.508826 | − | 0.860870i | \(-0.669920\pi\) | ||||
−0.508826 | + | 0.860870i | \(0.669920\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.14931 | 0.0960242 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.09246 | −0.271649 | −0.135825 | − | 0.990733i | \(-0.543368\pi\) | ||||
−0.135825 | + | 0.990733i | \(0.543368\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.87090 | 0.348871 | 0.174436 | − | 0.984669i | \(-0.444190\pi\) | ||||
0.174436 | + | 0.984669i | \(0.444190\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.98168 | 0.397326 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.14931 | −0.271499 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.2139 | −0.669105 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.5693 | 1.12237 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.7938 | 0.867184 | 0.433592 | − | 0.901109i | \(-0.357246\pi\) | ||||
0.433592 | + | 0.901109i | \(0.357246\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.1878 | −1.18884 | −0.594421 | − | 0.804154i | \(-0.702619\pi\) | ||||
−0.594421 | + | 0.804154i | \(0.702619\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.7895 | −1.34121 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.50479 | 0.326295 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.53707 | −0.413873 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.89692 | −0.125479 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.5510 | −0.929995 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.81215 | 0.121128 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.0558 | −1.63615 | −0.818074 | − | 0.575114i | \(-0.804958\pi\) | ||||
−0.818074 | + | 0.575114i | \(0.804958\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.607876 | −0.0260865 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.3353 | −0.441904 | −0.220952 | − | 0.975285i | \(-0.570916\pi\) | ||||
−0.220952 | + | 0.975285i | \(0.570916\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.4200 | 0.487395 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.4479 | −1.63794 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −37.7572 | −1.60560 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.25240 | −0.0530657 | −0.0265329 | − | 0.999648i | \(-0.508447\pi\) | ||||
−0.0265329 | + | 0.999648i | \(0.508447\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.270718 | 0.0114502 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.2847 | −0.687539 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 45.1868 | 1.90440 | 0.952198 | − | 0.305480i | \(-0.0988171\pi\) | ||||
0.952198 | + | 0.305480i | \(0.0988171\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.76156 | −0.115975 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.8603 | −0.664897 | −0.332449 | − | 0.943121i | \(-0.607875\pi\) | ||||
−0.332449 | + | 0.943121i | \(0.607875\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.5789 | −1.23784 | −0.618920 | − | 0.785454i | \(-0.712429\pi\) | ||||
−0.618920 | + | 0.785454i | \(0.712429\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.2803 | −0.888997 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.8401 | −1.11737 | −0.558683 | − | 0.829381i | \(-0.688693\pi\) | ||||
−0.558683 | + | 0.829381i | \(0.688693\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.45856 | −0.309967 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.37380 | −0.347404 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.6883 | 0.608326 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.4359 | 0.967302 | 0.483651 | − | 0.875261i | \(-0.339310\pi\) | ||||
0.483651 | + | 0.875261i | \(0.339310\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −52.2128 | −2.15139 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.45856 | 0.306804 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 43.2880 | 1.77763 | 0.888813 | − | 0.458271i | \(-0.151531\pi\) | ||||
0.888813 | + | 0.458271i | \(0.151531\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.3372 | 0.791417 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.58767 | 0.146588 | 0.0732940 | − | 0.997310i | \(-0.476649\pi\) | ||||
0.0732940 | + | 0.997310i | \(0.476649\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.0646 | 1.26715 | 0.633575 | − | 0.773681i | \(-0.281587\pi\) | ||||
0.633575 | + | 0.773681i | \(0.281587\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.4340 | 0.506351 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.2697 | 1.22861 | 0.614304 | − | 0.789069i | \(-0.289437\pi\) | ||||
0.614304 | + | 0.789069i | \(0.289437\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.2663 | −0.699668 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.38776 | 0.137054 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.0558 | 1.86018 | 0.930088 | − | 0.367336i | \(-0.119730\pi\) | ||||
0.930088 | + | 0.367336i | \(0.119730\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.43835 | 0.0579059 | 0.0289530 | − | 0.999581i | \(-0.490783\pi\) | ||||
0.0289530 | + | 0.999581i | \(0.490783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.2620 | −1.45749 | −0.728746 | − | 0.684784i | \(-0.759897\pi\) | ||||
−0.728746 | + | 0.684784i | \(0.759897\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.52311 | −0.221635 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.09246 | 0.244089 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −27.6156 | −1.10286 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.25240 | −0.129682 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.8401 | 1.38696 | 0.693480 | − | 0.720475i | \(-0.256076\pi\) | ||||
0.693480 | + | 0.720475i | \(0.256076\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.02791 | −0.319081 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.626198 | −0.0248109 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.89692 | 0.351957 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.8882 | −1.18051 | −0.590256 | − | 0.807216i | \(-0.700973\pi\) | ||||
−0.590256 | + | 0.807216i | \(0.700973\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.8603 | −0.743777 | −0.371888 | − | 0.928278i | \(-0.621290\pi\) | ||||
−0.371888 | + | 0.928278i | \(0.621290\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.50479 | 0.255730 | 0.127865 | − | 0.991792i | \(-0.459188\pi\) | ||||
0.127865 | + | 0.991792i | \(0.459188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −42.8294 | −1.68120 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.4479 | −0.918997 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.1589 | −1.10194 | −0.550971 | − | 0.834524i | \(-0.685743\pi\) | ||||
−0.550971 | + | 0.834524i | \(0.685743\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.25240 | −0.126888 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.2139 | 1.17697 | 0.588483 | − | 0.808510i | \(-0.299726\pi\) | ||||
0.588483 | + | 0.808510i | \(0.299726\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.0356 | 1.40162 | 0.700811 | − | 0.713347i | \(-0.252822\pi\) | ||||
0.700811 | + | 0.713347i | \(0.252822\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.62620 | 0.140830 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34.5327 | −1.33711 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.5048 | 0.638112 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51.2855 | 1.97986 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.68305 | −0.0648769 | −0.0324385 | − | 0.999474i | \(-0.510327\pi\) | ||||
−0.0324385 | + | 0.999474i | \(0.510327\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.50479 | −0.173133 | −0.0865666 | − | 0.996246i | \(-0.527590\pi\) | ||||
−0.0865666 | + | 0.996246i | \(0.527590\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −49.0375 | −1.88189 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.69701 | −0.103350 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −35.5650 | −1.36086 | −0.680428 | − | 0.732815i | \(-0.738206\pi\) | ||||
−0.680428 | + | 0.732815i | \(0.738206\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.5616 | −0.402952 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.27072 | −0.124604 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.29237 | 0.239373 | 0.119686 | − | 0.992812i | \(-0.461811\pi\) | ||||
0.119686 | + | 0.992812i | \(0.461811\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.4017 | −0.471102 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.5048 | −0.397897 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.2158 | 0.953747 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.9065 | −1.39394 | −0.696970 | − | 0.717101i | \(-0.745469\pi\) | ||||
−0.696970 | + | 0.717101i | \(0.745469\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.51542 | −0.208018 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.1064 | −0.605744 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.25240 | −0.197258 | −0.0986289 | − | 0.995124i | \(-0.531446\pi\) | ||||
−0.0986289 | + | 0.995124i | \(0.531446\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.6724 | 0.512756 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −46.8959 | −1.75626 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.51875 | −0.318138 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.6339 | −0.844102 | −0.422051 | − | 0.906572i | \(-0.638690\pi\) | ||||
−0.422051 | + | 0.906572i | \(0.638690\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.55102 | −0.355699 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.45856 | 0.277387 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.5606 | 1.28178 | 0.640891 | − | 0.767632i | \(-0.278565\pi\) | ||||
0.640891 | + | 0.767632i | \(0.278565\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.981678 | 0.0363087 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.4942 | −0.424547 | −0.212273 | − | 0.977210i | \(-0.568087\pi\) | ||||
−0.212273 | + | 0.977210i | \(0.568087\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 55.8390 | 2.05686 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.4619 | 0.752703 | 0.376351 | − | 0.926477i | \(-0.377179\pi\) | ||||
0.376351 | + | 0.926477i | \(0.377179\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.14931 | 0.225901 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.2836 | −1.25774 | −0.628872 | − | 0.777509i | \(-0.716483\pi\) | ||||
−0.628872 | + | 0.777509i | \(0.716483\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.03228 | 0.110945 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.29862 | −0.0839899 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.6358 | −0.862482 | −0.431241 | − | 0.902237i | \(-0.641924\pi\) | ||||
−0.431241 | + | 0.902237i | \(0.641924\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.64452 | −0.351466 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.54913 | 0.274378 | 0.137189 | − | 0.990545i | \(-0.456193\pi\) | ||||
0.137189 | + | 0.990545i | \(0.456193\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24.8034 | −0.900307 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.2418 | 1.74876 | 0.874381 | − | 0.485239i | \(-0.161268\pi\) | ||||
0.874381 | + | 0.485239i | \(0.161268\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.5510 | 1.21463 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.53707 | 0.344364 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.0558 | 0.867475 | 0.433737 | − | 0.901039i | \(-0.357195\pi\) | ||||
0.433737 | + | 0.901039i | \(0.357195\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.3555 | −0.480986 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.8863 | 1.36268 | 0.681338 | − | 0.731969i | \(-0.261399\pi\) | ||||
0.681338 | + | 0.731969i | \(0.261399\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.47689 | −0.0888578 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.8140 | −0.638254 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.9546 | 1.42969 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.25240 | 0.223442 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.3213 | −0.510500 | −0.255250 | − | 0.966875i | \(-0.582158\pi\) | ||||
−0.255250 | + | 0.966875i | \(0.582158\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.25240 | 0.329394 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.4402 | 0.442324 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.4200 | −0.405537 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.97398 | 0.282453 | 0.141226 | − | 0.989977i | \(-0.454895\pi\) | ||||
0.141226 | + | 0.989977i | \(0.454895\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.2847 | 0.434600 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.20617 | −0.0779511 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.6060 | −0.515434 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.2986 | 0.890554 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.42192 | 0.260941 | 0.130470 | − | 0.991452i | \(-0.458351\pi\) | ||||
0.130470 | + | 0.991452i | \(0.458351\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −54.6391 | −1.91864 | −0.959319 | − | 0.282323i | \(-0.908895\pi\) | ||||
−0.959319 | + | 0.282323i | \(0.908895\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31.3309 | 1.09882 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.66473 | 0.0582416 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.76156 | 0.0964966 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.12910 | −0.0743062 | −0.0371531 | − | 0.999310i | \(-0.511829\pi\) | ||||
−0.0371531 | + | 0.999310i | \(0.511829\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.3188 | −1.26600 | −0.632998 | − | 0.774154i | \(-0.718176\pi\) | ||||
−0.632998 | + | 0.774154i | \(0.718176\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.0419 | 0.766471 | 0.383235 | − | 0.923651i | \(-0.374810\pi\) | ||||
0.383235 | + | 0.923651i | \(0.374810\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.9344 | 1.69956 | 0.849781 | − | 0.527136i | \(-0.176734\pi\) | ||||
0.849781 | + | 0.527136i | \(0.176734\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.0096 | 0.798194 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.27072 | −0.0786757 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.49084 | 0.293486 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.2986 | 0.355548 | 0.177774 | − | 0.984071i | \(-0.443110\pi\) | ||||
0.177774 | + | 0.984071i | \(0.443110\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0925 | 0.348016 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.19554 | −0.316711 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.3169 | −0.869901 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.93545 | −0.340984 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.95377 | −0.169813 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.0356 | 0.822963 | 0.411482 | − | 0.911418i | \(-0.365011\pi\) | ||||
0.411482 | + | 0.911418i | \(0.365011\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.0096 | −0.512718 | −0.256359 | − | 0.966582i | \(-0.582523\pi\) | ||||
−0.256359 | + | 0.966582i | \(0.582523\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.2707 | −0.828106 | −0.414053 | − | 0.910253i | \(-0.635887\pi\) | ||||
−0.414053 | + | 0.910253i | \(0.635887\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.00000 | −0.272639 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.4985 | 1.44667 | 0.723333 | − | 0.690499i | \(-0.242609\pi\) | ||||
0.723333 | + | 0.690499i | \(0.242609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.85069 | −0.130776 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 61.4007 | 2.08287 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.4340 | −0.421309 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.7572 | 0.600990 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.56165 | −0.154036 | −0.0770179 | − | 0.997030i | \(-0.524540\pi\) | ||||
−0.0770179 | + | 0.997030i | \(0.524540\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.7938 | 0.802546 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.10308 | 0.205618 | 0.102809 | − | 0.994701i | \(-0.467217\pi\) | ||||
0.102809 | + | 0.994701i | \(0.467217\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.0096 | 0.437807 | 0.218904 | − | 0.975746i | \(-0.429752\pi\) | ||||
0.218904 | + | 0.975746i | \(0.429752\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.4307 | −0.383804 | −0.191902 | − | 0.981414i | \(-0.561466\pi\) | ||||
−0.191902 | + | 0.981414i | \(0.561466\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.2986 | 0.613716 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.49084 | 0.150449 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.8324 | 0.697129 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.52311 | 0.184411 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 53.0881 | 1.77059 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.8603 | −0.395123 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.747604 | 0.0248787 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.8863 | −0.660313 | −0.330157 | − | 0.943926i | \(-0.607102\pi\) | ||||
−0.330157 | + | 0.943926i | \(0.607102\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.83237 | 0.193447 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.8217 | −1.91572 | −0.957860 | − | 0.287236i | \(-0.907264\pi\) | ||||
−0.957860 | + | 0.287236i | \(0.907264\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.6175 | 0.450672 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.04623 | −0.100595 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.17722 | −0.269742 | −0.134871 | − | 0.990863i | \(-0.543062\pi\) | ||||
−0.134871 | + | 0.990863i | \(0.543062\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.0664 | −0.825967 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.89692 | −0.292846 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.45856 | 0.113594 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.7312 | −0.483314 | −0.241657 | − | 0.970362i | \(-0.577691\pi\) | ||||
−0.241657 | + | 0.970362i | \(0.577691\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.85069 | −0.126201 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.3632 | 0.601183 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.9431 | −0.618846 | −0.309423 | − | 0.950925i | \(-0.600136\pi\) | ||||
−0.309423 | + | 0.950925i | \(0.600136\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.7293 | −0.350137 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.3353 | 0.402118 | 0.201059 | − | 0.979579i | \(-0.435562\pi\) | ||||
0.201059 | + | 0.979579i | \(0.435562\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0000 | −0.521032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.1710 | 0.590477 | 0.295238 | − | 0.955424i | \(-0.404601\pi\) | ||||
0.295238 | + | 0.955424i | \(0.404601\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.25240 | 0.105577 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.20617 | −0.266103 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.4113 | −1.21187 | −0.605935 | − | 0.795514i | \(-0.707201\pi\) | ||||
−0.605935 | + | 0.795514i | \(0.707201\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28.0785 | 0.907649 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −56.4681 | −1.82345 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.0943 | 1.32562 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.832365 | 0.0268226 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.4821 | −1.23750 | −0.618750 | − | 0.785588i | \(-0.712361\pi\) | ||||
−0.618750 | + | 0.785588i | \(0.712361\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22.2986 | 0.716335 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.5896 | −1.43095 | −0.715473 | − | 0.698640i | \(-0.753789\pi\) | ||||
−0.715473 | + | 0.698640i | \(0.753789\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45.7572 | −1.46691 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.2524 | 1.06384 | 0.531919 | − | 0.846795i | \(-0.321471\pi\) | ||||
0.531919 | + | 0.846795i | \(0.321471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.90754 | −0.316646 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.1493 | −0.387898 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.9186 | 0.348248 | 0.174124 | − | 0.984724i | \(-0.444291\pi\) | ||||
0.174124 | + | 0.984724i | \(0.444291\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.35548 | 0.297788 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.49521 | 0.0475448 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.3738 | 0.551897 | 0.275949 | − | 0.961172i | \(-0.411008\pi\) | ||||
0.275949 | + | 0.961172i | \(0.411008\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.7110 | 0.974583 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.0752 | 0.382425 | 0.191212 | − | 0.981549i | \(-0.438758\pi\) | ||||
0.191212 | + | 0.981549i | \(0.438758\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.896916 | 0.0283772 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7800.2.a.bn.1.1 | yes | 3 | |
5.4 | even | 2 | 7800.2.a.bm.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7800.2.a.bm.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
7800.2.a.bn.1.1 | yes | 3 | 1.1 | even | 1 | trivial |